.TH "snaphu" 1
.SH NAME
snaphu \- phase unwrapping algorithm for SAR interferometry
.SH SYNOPSIS
.B snaphu
[options]
[infile]
[linelength]
[options]
.SH DESCRIPTION
\fBsnaphu\fR is a \fBs\fRtatistical-cost \fBn\fRetwork-flow
\fBa\fRlgorithm for \fBph\fRase \fBu\fRnwrapping.  Given an input
interferogram and other observable data, \fBsnaphu\fR attempts to
compute congruent phase-unwrapped solutions that are maximally
probable in an approximate \fIa posteriori\fR sense.  The algorithm's
solver routine is based on network optimization.  By default,
\fBsnaphu\fR assumes that its input is a synthetic aperture radar
(SAR) interferogram measuring surface topography.  Deformation
measurements are assumed if the \fB\-d\fR option is given.  Smooth,
generic data are assumed if the \fB\-s\fR option is given.
.PP
This man page documents only the syntax and usage of \fBsnaphu\fR.  Its
theoretical foundations are discussed in the references cited below.
.PP
The most common input parameters may be given on the command line,
while many other twiddle parameters are handled via the \fB\-f\fR
option and configuration files.  At the very least, the name of a
wrapped-phase input file and its line length must be specified.  Range
should increase towards the right in the interferogram, and the
flat-earth phase ramp should be removed from the input interferogram
before \fBsnaphu\fR is run.  For deformation interferograms, phase
variations due to topography should be removed as well.
.PP
Except for the input file name and the line length, all input
parameters take default values if not specified.  However, these
parameters should be customized whenever possible since the accuracy
of the solution depends on how well the statistics of the estimation
problem are modeled.  To avoid poor-quality solutions, users are
strongly encouraged to provide their best estimates of the relevant
problem parameters.  Parameters are set in the order in which they are
given on the command line, so multiple configuration files or options
may be given, with later values overriding earlier ones.
.PP
Allowable file formats are detailed below.  The default format for the
input file is COMPLEX_DATA, but any of the described formats may be
used.  If either of the ALT_LINE_DATA or ALT_SAMPLE_DATA formats are
used, the magnitude and phase (in radians from 0 to 2pi) of the
interferogram should be in the first and second channels of the file,
respectively.  If the FLOAT_DATA format is used, the input file should
contain only the phase of the interferogram (in radians from 0 to
2pi); the magnitude may be passed with the \fB\-m\fR option.
.SH OPTIONS
.TP
\fB\-a\fP \fIampfile\fP 
Read brightness data from the file \fIampfile\fP.  The file should
contain the amplitudes (not powers) of the two individual SAR images
forming the interferogram if the formats ALT_SAMPLE_DATA (default) or
ALT_LINE_DATA are used.  It should contain an average of those two
images if the FLOAT_DATA format is used.  If (1) the amplitudes of
both images are available, (2) the interferogram magnitude is also
available, and (3) the \fB\-c\fP option is not used, then a coherence
estimate is automatically formed from the available data.  The number
of looks used for this estimate can be set in a configuration file.
If no amplitude or power data are specified, then the magnitude of the
input interferogram is used as the average amplitude, and no coherence
estimate is formed.  Note that the magnitude of the interferogram is
not equal to the average amplitude of the SAR images.  The amplitude
data should be in the same system of units used for the input
interferogram, and also coregistered to it.
.TP
\fB\-A\fP \fIpwrfile\fP
Similar to the \fB\-a\fP option, except the data in the specified file
is assumed to represent the powers of the two individual SAR images.
.TP
\fB\-b\fP \fIBperp\fP
For topography mode, use \fIBperp\fP (decimal value, in meters) as the
value of the perpendicular component of the interferometric baseline.
The sign is defined such that \fIBperp\fP is negative if the unwrapped
phase increases with the elevation.  By default, repeat-pass or
ping-pong mode is assumed; for single-antenna-transmit data, the value
of \fIBperp\fP should be halved, or the transmit mode should be set
accordingly in a configuration file (see the \fB\-f\fP option).  The
baseline value is only used in topography mode.
.TP
\fB\-c\fP \fIcorrfile\fP
Read correlation data from the file \fIcorrfile\fP.  The correlation
data should be the same size as, and registered to, the input
interferogram.  Consequently, a raw correlation estimate may need to
be upsampled if it incorporates more looks than the interferogram.
If the \fB\-c\fP option is not given, a coherence estimate is formed
from the available data if possible.  Otherwise, a uniform default
coherence is assumed for the entire interferogram.  If the
ALT_LINE_DATA (default) or ALT_SAMPLE_DATA formats are used, the
correlation data should be in the second data channel of the file; the
first channel is ignored.  The FLOAT_DATA format may also be used.
The correlation values should be between zero and one, inclusive.
.TP
\fB\-C\fP \fIconfigstr\fP
Parse the string \fIconfigstr\fP as if it were a line from a
configuration file containing a keyword-value pair (see the \fB-f\fP
option).  Configuration lines generally have whitespace between the
keyword and the value, so \fIconfigstr\fP will usually need to be
surrounded by quotation marks on a command line so that the shell does
not split it into separate arguments (\fBsnaphu\fR itself does not
require or allow quotation marks, however).  The syntax for how
quotation marks are handled is defined by the shell.  Multiple
instances of the \fB-C\fP option may be used in order to specify
multiple configuration inputs.  Later instances of the \fB-C\fP option
take precedence over both earlier instances of the \fB-C\fP option and
the configurations specified by earlier instances of the \fB-f\fP
option.
.TP
.B \-d
Run in deformation mode.  The problem statistics and resulting cost
functions are based on the assumption that the true unwrapped phase
represents surface displacement rather than elevation.
.TP
\fB\-e\fP \fIestimatefile\fP
Flatten using the unwrapped phase estimate in the file
\fIestimatefile\fP.  The estimate is subtracted from the input
interferogram before unwrapping, and is inserted back into the
solution just before the output is written.  The estimate also affects
the cost functions used, since subtracting a constant from a random
variable shifts the probability density function of the random
variable.  If the formats ALT_LINE_DATA (default) or ALT_SAMPLE_DATA
are used, the unwrapped estimate (in radians) should be in the second
data channel of the file; the first channel is ignored.  The
FLOAT_DATA format may also be used.
.TP
\fB\-f\fP \fIconfigfile\fP 
Read configuration parameters from file \fIconfigfile\fP.  The file is
parsed line by line for key-value pairs.  Template configuration files
are included with the \fBsnaphu\fP source code: \fIsnaphu.conf.full\fP
contains all valid key-value pairs; \fIsnaphu.conf.brief\fP contains
the most important parameters.  Lines not beginning with alphanumeric
characters are treated as comment lines.  Command line options
specified after \fB\-f\fP will override parameters specified in the
\fIconfigfile\fP and vice versa.  The \fB\-f\fP option may be given
multiple times with different configuration files, with parameters in
later-specified files overriding those in earlier ones.
.TP
.B \-g \fImaskfile\fP
Grow a connected component mask for the unwrapped solution and write
the mask to the file \fImaskfile\fP.  A connected component is a
region of pixels in the solution that is believed to have been
unwrapped in a relative, internally self-consistent manner according
to the statistical costs used.  Regions that are smaller than a
preselected threshold are masked out.  Parameters for this option can
be set in the configuration file.  The connected component file is
composed of unsigned characters by default, with all pixels of the same value
belonging to the same connected component and zero corresponding to
masked pixels.
.TP
.B \-G \fImaskfile\fP
Grow a connected component mask (see the \fB\-g\fP option) for the
input data array, assuming that it is already unwrapped, and write the
mask to the file \fImaskfile\fP.  Statistical cost functions are
computed for forming the mask, but a new unwrapped solution is not
computed.
.TP
.B \-h, \-\-help
Print a help message summarizing command-line options and exit.
.TP
.B \-i
Run in initialize-only mode.  Normally, \fBsnaphu\fP uses either an
approximate minimum spanning tree (MST) algorithm or a minimum cost
flow (MCF) algorithm for generating the initialization to its
iterative, modified network-simplex solver.  If \fB\-i\fP is given,
the initialization is written to the output and the program exits
without running the iterative solver.
.TP
.B \-k
Keep temporary tile outputs.  If this option is specified when
\fBsnaphu\fP runs in tile mode, the temporary directory where tile
outputs are stored will be left in place rather than deleted.  The
tile-mode initialization of the \fB-S\fP option will also be left in
place rather than deleted.
.TP
\fB\-l\fP \fIlogfile\fP
Log all runtime parameters and some other environment information into
the specified file.  The log file is a text file in the same format as
a configuration file.
.TP
\fB\-m\fP \fImagfile\fP
Read interferogram magnitude data from the specified file.  This
option is useful mainly if the wrapped-phase input file is given as a
set of real phase values rather than complex interferogram values.
The interferogram magnitude is used to form a coherence estimate if
appropriate amplitude data are given as well.  The default file format
is FLOAT_DATA.  If the formats ALT_LINE_DATA or ALT_SAMPLE_DATA are
used, the magnitude should be in the first data channel of the file;
the second channel is ignored.  If the COMPLEX_DATA format is used,
the phase information is ignored.  Areas where the magnitude is zero
are treated as masked areas (see the \fB\-M\fP option).
.TP
\fB\-M\fP \fIbytemaskfile\fP
Read a byte mask from the specified file.  The mask file should be the
same size as the input array to be unwrapped.  The mask should have
the binary (not ASCII) value 0 where pixels of the input array are to
be ignored during the primary optimization stage of the program.
Values elsewhere should be binary 1.  Masking is not applied until
after the initialization stage of \fBsnaphu\fP.  Masked areas are
treated as areas in which the solution phase value is irrelevant to
the solution cost.  The magnitude of the interferogram is set to zero
in masked areas in the output file.  Areas with zero magnitude in the
input data are treated as masked areas as well.  Areas near the edges
of the input may also be masked via options in a configuration file.
.TP
.B \-n
Run in no-statistical-costs mode.  If the \fB\-i\fP or \fB\-p\fP
options are given, \fBsnaphu\fP will not use statistical costs.
Information from a weight file (\fB\-w\fP option) will still be used
if given.
.TP
\fB\-o\fP \fIoutfile\fP
Write the unwrapped output to a file called \fIoutfile\fP.  If the
file formats ALT_LINE_DATA (default) or ALT_SAMPLE_DATA are used, the
unwrapped phase is written into the second data channel, while the
interferogram magnitude is written into the first channel.  The format
FLOAT_DATA may also be used.
.TP
\fB\-p\fP \fIvalue\fP
Run in Lp-norm mode with p=\fIvalue\fP, where \fIvalue\fP is a
nonnegative decimal.  Instead of statistical cost functions, the
program uses Lp cost functions with statistically based weights
(unless \fB\-n\fP is also given).  Solutions are still always
congruent.  Moreover, congruence is enforced within the solver
routine, not as a post-optimization processing step.  Therefore, if
p=2, for example, least-squares cost functions are used, but the
solution will probably be more accurate than one generated from a
transform-based least-squares algorithm.
.TP
.B \-q
Run in quantify-only mode.  The input data are assumed to be unwrapped
already, and the total cost of this solution is calculated and
printed.  The unwrapped phase is wrapped assuming congruence for the
cost calculation.  Round-off errors may limit the precision of the
quantified cost.  See the \fB\-u\fP option for allowable file formats.
.TP
.B \-s
Run in smooth-solution mode.  The problem statistics and resulting
cost functions are based on the assumption that the true unwrapped
phase represents a generic surface with no discontinuities.  This is
the same as deformation mode with the DEFOMAX parameter set to zero.
.TP
.B \-S
Do single-tile re-optimization after tile-mode initialization.  If
this option is specified, \fBsnaphu\fP will run in tile mode to
generate an unwrapped solution, which is then used as the
initialization to a single-tile optimization that produces the final
unwrapped output.  The tile-mode initialization may itself be
initialized by the MST or MCF algorithms (or an input unwrapped phase
file) as normal.  This option is equivalent to running an instance of
\fBsnaphu\fP in tile mode, then running another instance of
\fBsnaphu\fP taking the tile-mode output as an unwrapped input via the
\fB-u\fP option.  Tile parameters must be specified when using this
option.  This approach is often faster than unwrapping an
interferogram as a single tile from an MST initialization, especially
if multiple processors are used.
.TP
.B \-t
Run in topography mode.  The problem statistics and resulting cost
functions are based on the assumption that the true unwrapped phase
represents surface elevation.  This is the default.
.TP
.B \-u
Assume that the input file is unwrapped rather than wrapped.  The
algorithm makes iterative improvements to this solution instead of
using an initialization routine.  The input file may be in the formats
ALT_LINE_DATA (default) or ALT_SAMPLE_DATA; the interferogram
magnitude should be in the first data channel and the unwrapped phase
should be in the second data channel.  The format FLOAT_DATA may also
be used.
.TP
.B \-v
Run in verbose mode.  Extra information on the algorithm's progress is
printed to the standard output.
.TP
\fB\-w\fP \fIweightfile\fP
Read external, scalar weights from file \fIweightfile\fP.  The
weights, which should be positive short integers, are applied to
whichever cost functions are used.  There is one weight value for each
arc in the network, so \fIweightfile\fP should be the concatenation of
raster horizontal-flow and vertical-flow arc weights.  Thus, for an N
row by M column interferogram, \fIweightfile\fP would consist of a
rasterized (N-1) by M array followed by a rasterized N by (M-1) array
of short integer data.  This option is not well tested.
.TP
\fB\-\-aa\fP \fIampfile1 ampfile2\fP 
Amplitude data are read from the files specified.  The data from the
two individual SAR images forming the interferogram are assumed to be
separately stored in files \fIampfile1\fP and \fIampfile2\fP.  These
files should be in the format FLOAT_DATA.  This option is similar to
the \fB\-a\fP option.
.TP
\fB\-\-AA\fP \fIpwrfile1 pwrfile2\fP
Similar to the \fB\-\-aa\fP option, but power data are read from the
specified files.
.TP
\fB\-\-assemble
Assemble the tile-mode temporary files from a previous tile-mode run
of \fBsnaphu\fP, possibly with different secondary optimization
parameters, to produce a new unwrapped solution.  The tile directory
name must be specified with the \fB\-\-tiledir\fP option.  Most
configuration options (from the command line and any configuration
files) must be specified similar to the previous run, including the
output file name from which the names of temporary tile files are
derived.  The previous output file may hence be overwritten by the new
output file.  This option is useful if the user wishes to modify
tile-assembly parameters without unwrapping the individual tiles over
again.
.TP
.B \-\-copyright, \-\-info
Print the software copyright notice and bug report info, then exit.
.TP
\fB\-\-costinfile\fP \fIcostfile\fP
Read statistical cost arrays from file \fIcostfile\fP.  This file
should be in the format written by the \fB\-\-costoutfile\fP option.
The cost file does not control whether \fBsnaphu\fP runs in
topography, deformation, or smooth-solution mode; the latter two must
be specified explicitly even if \fIcostfile\fP was generated while
running in those modes.
.TP
\fB\-\-costoutfile\fP \fIcostfile\fP
Write statistical cost arrays to file \fIcostfile\fP.  This option can
be used with the \fB\-\-costinfile\fP option to save the time of
generating statistical costs if the same costs are used multiple times.
.TP
.B \-\-debug, \-\-dumpall
Dump all sorts of intermediate arrays to files.  
.TP
.B \-\-mst
Use a minimum spanning tree (MST) algorithm for the initialization.
This is the default.
.TP
.B \-\-mcf
Use a minimum cost flow (MCF) algorithm for the initialization.  The
cs2 solver by Goldberg and Cherkassky is used.  The modified
network-simplex solver in L1 mode may give different results than the
cs2 solver, though in principle both should be L1 optimal.
.TP
.B \-\-nproc \fIn\fP
Use \fIn\fP parallel processes when in tile mode.  The program forks a
new process for each tile so that tiles can be unwrapped in parallel;
at most \fIn\fP processes will run concurrently.  Forking is done
before data are read.  The standard output streams of child processes
are directed to log files in the temporary tile directory.
.TP
.B \-\-piece \fIfirstrow firstcol nrow ncol\fP
Read and unwrap only a subset or part of the input interferogram.  The
read piece is the \fInrow\fP by \fIncol\fP rectangle whose upper left
corner is the pixel at row \fIfirstrow\fP and column \fIfirstcol\fP
(indexed from 1).  All input files (such as amplitude, coherence,
etc.) are assumed to be the same size as the input phase file.  All
output files are \fInrow\fP by \fIncol\fP.
.TP
.B \-\-tile \fIntilerow ntilecol rowovrlp colovrlp\fP
Unwrap the interferogram in tile mode.  The interferogram is
partitioned into \fIntilerow\fP by \fIntilecol\fP tiles, each of which
is unwrapped independently.  Tiles overlap by \fIrowovrlp\fP and
\fIcolovrlp\fP pixels in the row and column directions.  The tiles are
then segmented into reliable regions based on the cost functions, and
the regions are reassembled.  The program creates a subdirectory for
temporary files in the directory of the eventual output file (see the
\fB\-\-tiledir\fP and \fB-k\fP options).  Tiles can be unwrapped in
parallel (see the \fB\-\-nproc\fP option).
.TP
.B \-\-tiledir \fIdirname\fP
Use \fIdirname\fP as the name of the directory in which temporary
tile-model outputs are written and/or read.  The directory is created
if it does not exist, and it is removed at the end of the run unless
the \fB-k\fP or \fB\-\-assemble\fP options are specified.
.SH FILE FORMATS
The formats of input files may be specified in a configuration file.
All of these formats are composed of raster, single-precision (float,
real*4, or complex*8) floating-point data types in the platform's
native byte order.  Data are read line by line in row-major order
(across then down, with the column index varying faster than the row
index).  Regardless of the file format, all input data arrays should
have the same number of samples in width and depth and should be
coregistered to one another.  Note that weight files and cost files
have their own formats.  The allowable formats for other data files
are described below.
.TP
COMPLEX_DATA
Alternating floats correspond to the real (in-phase) and imaginary
(quadrature) components of complex data samples.  The specified line
length should be the number of complex samples (pairs of real and
imaginary samples) per line.
.TP
ALT_LINE_DATA
Alternating lines (rows) of data correspond to lines of purely real
data from two separate arrays.  The first array is often the magnitude
of the interferogram, and the second may be unwrapped phase,
coherence, etc.  This is also sometimes called \fBhgt\fP, \fBrmg\fP,
or line-interleaved format.
.TP
ALT_SAMPLE_DATA
Alternating samples correspond to purely real samples from two
separate arrays.  This format is sometimes used for the amplitudes of
the two SAR images.
.TP
FLOAT_DATA
The file contains data for only one channel or array, and the data are
purely real.
.SH EXAMPLES
Unwrap a wrapped topographic interferogram called ``wrappedfile''
whose line length is 1024 complex samples (output will be written to a
file whose name is compiled into the program):
.PP
.nf
    snaphu wrappedfile 1024
.fi
.PP
Unwrap the same file as above, but use brightness information from the
file ``ampfile,'' set the perpendicular baseline to -165 m at
midswath, and place the output in a file called ``unwrappedfile''
(coherence data are generated automatically if ``wrappedfile''
contains complex data and ``ampfile'' contains amplitude data from
both SAR images):
.PP
.nf
    snaphu wrappedfile 1024 -a ampfile \e 
        -b -165 -o unwrappedfile
.fi
.PP
Unwrap the interferogram as above, but read correlation
information from the file ``corrfile'' instead of generating it from
the interferogram and amplitude data:
.PP
.nf
    snaphu wrappedfile 1024 -a ampfile -c corrfile \e 
        -b -165 -o unwrappedfile
.fi
.PP
The following is equivalent to the previous example, but input
parameters are read from a configuration file, and verbose output is
displayed:
.PP
.nf
    cat > configfile
    # This is a comment line which will be ignored
    AMPFILE      ampfile
    CORRFILE     corrfile
    BPERP        -165
    OUTFILE      unwrappedfile
    EOF (ie, Ctrl-D)

    snaphu -v -f configfile wrappedfile 1024
.fi
.PP
Unwrap the same interferogram, but use only the MST initialization
(with scalar statistical weights) and write the output to ``mstfile'':
.PP
.nf
    snaphu -f configfile -i wrappedfile 1024 -o mstfile
.fi
.PP
Read the unwrapped data in ``mstfile'' and use that as the
initialization to the modified network-simplex solver:
.PP
.nf
    snaphu -f configfile -u mstfile 1024 -o unwrappedfile
.fi
.PP
Note that in the previous two examples, the output file name in the
configuration file is overrided by the one given on the command line.
The previous two commands together are in principle equivalent to the
preceding one, although round-off errors in flow-to-phase conversions
may cause minor differences
.PP
Unwrap the interferogram as above, but use the MCF algorithm for
initialization:
.PP
.nf
    snaphu -f configfile wrappedfile 1024 --mcf
.fi
.PP
Unwrap the interferogram once again, but first flatten it with the
unwrapped data in ``estfile,'' then reinsert the subtracted phase
after unwrapping:
.PP
.nf
    snaphu -f configfile wrappedfile 1024 -e estfile
.fi
.PP
The following assumes that the wrapped input interferogram measures
deformation, not topography.  Unwrap the interferogram with the given
correlation data:
.PP
.nf
    snaphu -d wrappedfile 1024 -c corrfile 
.fi
.PP
Unwrap the input interferogram by minimizing the unweighted congruent
L2 norm:
.PP
.nf
    snaphu -p 2 -n wrappedfile 1024
.fi
.PP
Unwrap the interferogram as a three-by-four set of tiles that overlap
by 30 pixels, with the specified configuration file, using two
processors:
.PP
.nf
    snaphu wrappedfile 1024 -f configfile \e
        --tile 3 4 30 30 --nproc 2
.fi
.PP
.SH "HINTS AND TIPS"
The program may print a warning message about costs being clipped to
avoid overflow.  If too many costs are clipped, the value of COSTSCALE
may need to be decreased in a configuration file (via the \fB\-f\fR
option).  If the program prints a warning message about an unexpected
increase in the total solution cost, this is an indication that too
many costs are clipped.  It is usually okay if just a few costs are
clipped.  
.PP
In topography mode, if the unwrapped result contains too many
discontinuities, try increasing the value of LAYMINEI or decreasing
the value of LAYCONST.  The former determines the normalized intensity
threshold for layover, and the latter is the relative layover
probability.  If there are too many discontinuities running in
azimuth, try decreasing the value of AZDZFACTOR, which affects the
ratio of azimuth to range costs.  If the baseline is not known, take a
guess at it and be sure its sign is correct.  Specify the SAR imaging
geometry parameters as well as possible.  The defaults assume ERS data
with five looks taken in azimuth.
.PP
In deformation mode, if the unwrapped result contains too many
discontinuities, try increasing the value of DEFOTHRESHFACTOR or
decreasing the value of DEFOCONST.  If the surface displacement varies
slowly and true discontinuities are not expected at all, DEFOMAX_CYCLE
can be set to zero.  This behavior is also invoked with the \fB\-s\fR
option.  The resulting cost functions will be similar to
correlation-weighted L2 cost functions, though the former are not
necessarily centered on the wrapped gradients.  Congruence is still
enforced during rather than after optimization.
.PP
The program can be run in initialize-only (\fB\-i\fR) mode for quick
down-and-dirty MST or MCF solutions.
.SH SIGNALS
Once the iterative solver has started, \fBsnaphu\fR traps the
interrupt (INT) and hangup (HUP) signals.  Upon receiving an
interrupt, for example if the user types Ctrl-C, the program finishes
a minor iteration, dumps its current solution to the output, and
exits.  If a second interrupt is given after the first (caught)
interrupt, the program exits immediately.  If a hangup signal is
received, the program dumps its current solution then continues to
execute normally.
.SH "EXIT STATUS"
Upon successful termination, the program exits with code 0.  Errors
result in exit code 1.
.SH FILES
The following files may be useful for reference, but are not required.
They are included in the program source distribution and may be installed
somewhere on the system.
.TP
\fIsnaphu.conf.full\fP
Template configuration file setting all valid input parameters (though
some may be commented out).
.TP
\fIsnaphu.conf.brief\fP
General-purpose template configuration file setting the most
important or commonly modified input parameters.
.PP
In addition to parameters read from configuration files specified on
the command line, default parameters may be read from a system-wide
configuration file if such a file is named when the program is
compiled.
.SH BUGS
The \fB\-w\fR option has not been tested exhaustively.
.PP
Extreme shadow discontinuities (i.e., abrupt elevation drops in
increasing range due to cliffs facing away from the radar) are not
modeled that well in the cost functions for topography mode.
.PP
Abrupt changes in surface reflectivity, such as those of coastlines
between bright land and dark water, might be misinterpreted as layover
and assigned inappropriate costs.
.PP
The algorithm's behavior may be unpredictable if the costs are badly
scaled and excessively clipped to fit into their short-integer data
types.
.PP
There is no error checking that ensures that the network node
potentials (incost and outcost) do not overflow their integer
data types.
.PP
Automatic flow clipping is built into the MST initialization, but it
can give erratic results and may loop infinitely for certain input
data sets.  It is consequently turned off by default.
.PP
Dedicated programs for specific Lp objective functions may work better
than \fBsnaphu\fR in Lp mode.  Note that \fBsnaphu\fR enforces
congruence as part of the problem formulation, however, not as a
post-optimization processing step.
.PP
A tree pruning capability is built into the code and can be enabled
from a configuration file, but this functionality is experimental and
not well tested.
.SH REFERENCES
C. W. Chen and H. A. Zebker, ``Two-dimensional phase unwrapping with
use of statistical models for cost functions in nonlinear
optimization,'' \fIJournal of the Optical Society of America A\fP,
\fB18\fP, 338-351 (2001).
.PP
C. W. Chen and H. A. Zebker, ``Network approaches to two-dimensional
phase unwrapping: intractability and two new algorithms,'' \fIJournal
of the Optical Society of America A\fP, \fB17\fP, 401-414 (2000).
.PP
C. W. Chen and H. A. Zebker, ``Phase unwrapping for large SAR
interferograms: Statistical segmentation and generalized network
models,'' \fIIEEE Transactions on Geoscience and Remote Sensing\fP,
\fB40\fP, 1709-1719 (2002). 
